Construction of recombinant nucleic acid molecules requires two enzymatic steps. First, site-specific restriction endonuclease digestion or PCR amplification are used to generate linear nucleic acid molecules with defined termini. Second, the linear molecules are covalently joined at their termini in the presence of a ligase enzyme. Methods of covalently joining and cloning nucleic acid molecules that require only one step or that eliminate the use of restriction endonucleases or ligases would be advantageous over the traditional method of constructing recombinant nucleic acid molecules.